Algebra 2 CP
Name________________
Assignment___________
For the given configuration, determine how many different computer passwords are possible if (a) digits and letters can be repeated. (b) digits and letters cannot be repeated.
1. 3 digits followed by 4 letters. 1a.________
1b.________
Evaluate the expression. You MUST show work!
2. 2 digits followed by 5 letters 2a.________
2b.________
3. 5 !
4. 5

3 !
5.
3 !
7 !
2 !
3._________
6.
14
P
7
7.
12
P
12
Find the number of distinguishable permutations of the letters in the word.
8. ASSASSIN 9. MISSISSIPPI
Evaluate the expression.
10.
29
C
3
11.
14
C
10
4._________
5._________
6. ________
7. ________
8._________
9._________
10.________
11.________
Find the number of possible 5-card hands that contain the cards specified.
12. 5 red cards 13. 4 spades and 1 card that isn’t a spade 12.________
14. 3 face cards and 2 non-face cards 15. 2 aces an d 3 cards that aren’t aces
13.________
14.________
15.________

16. A committee of six members needs to be chosen from a 52-member club.
How many ways can the committee be chosen?
16.________
17. A committee of 3 is selected from Jillian, Miles, Mark, Andrew, Kamila, and Nikia.
How many committees contain 2 boys and 1 girl?
17.________
18. A box of pencils contains 4 red, 2 white, and 3 blue pencils. How many different ways can
2 red, 1 white, and 1 blue pencil be selected?
18.________
19. In how many ways can a committee consisting of a president, vice-president, secretary,
and treasurer be formed from a group of 50 students?
19.________
Work out all terms, DO NOT leave terms in combinatoric form.
20. Expand using Pascal’s Triangle/Binomial Theorem

4 x

1

3
20. ______________________________________________
21. Expand using Pascal’s Triangle/Binomial Theorem

3 x
 y

6
21. _______________________________________________

22. Write the fourth term of the expansion of

2 x

2 y

15
22.________
23. Write the 7 term of the expansion of

2 x

5

9
23.________
Find the indicated probability given the following scenario.
Integers 1-80 are used to play a counting game
– each number is equally as likely to be chosen.
24. An odd number is chosen. 25. A number greater than
50 is chosen. 24.________
25.________
27. A perfect cube is chosen. 26.________ 26. A multiple of 3 is chosen.
27.________
Find the indicated odds given the following scenario.
You are rolling a 20-sided die.
28. In favor or rolling a 10. 29. In favor of rolling a number
less than 6.
30. Against rolling a 1, 3, or 5. 31. Against rolling a number
greater than 13.
32. In favor of rolling an even
number less than 10
33. Against rolling an odd number
greater than 10
28.________
29.________
30.________
31.________
32.________
33.________

Find the probability that a dart thrown at the square target shown will hit the given region. f e d c b a
24 in
34. The center a.
2 in
35. The border f 34.________
36. The center a or the ring b. 37. The four rings (b, c, d, and e)
or the center a
35.________
36.________
Calculate the following probabilities. Be Careful and USE YOUR NOTES!
37.________
38. Two dice are rolled. What is the probability that one die shows a multiple of 3 and the other a
multiple of 2?
38.________
39. Two cards are drawn at random from a standard deck. Find the probability of drawing a face
card then a diamond when replacement occurs.
39.________
40. Seven cards are drawn from a deck of 52 cards. What is the probability that five cards are
spades and two are hearts?
40.________
41. A basket contains 3 apples, 6 oranges, 7 pears, and 9 peaches. What is the probability of
selecting 1 apple and 2 oranges or 2 apples and 1 peach?
41.________

Calculate the following probabilities. Be Careful and USE YOUR NOTES!
Be sure to determine independent and dependent events; and exclusive and inclusive events.
42. Liz has 2 red, 2 white, and 3 blue marbles in a cup. She draws two marbles at random and does
not replace the first one. What is the probability that she will draw a white marble and then a blue
marble or a blue then a red?
42.________
43. Two cards are drawn at random from a standard deck without replacement. What is the
probability that one is a heart and the other a club, or a heart then a spade?
43.________
44. Seven coins are chosen from a bowl randomly. The bowl contains 8 nickels and 4 quarters.
What is the probability that the total value of the coins is $0.75?
44.________
45. There are 3 quarters, 4 dimes, and 7 nickels in a change purse. Suppose 3 coins are selected at
random. What is the probability of selecting two quarters, then a nickel when replacement doesn’t occur?
45.________
46. 5 cards are drawn from a standard deck of cards. What is the probability of drawing
at least 3 kings?
46.________
47. A card is drawn at random from a standard deck of cards. What is the probability of
drawing a five or an odd card?
47.________
48. A bag contains 45 dyed eggs: 15 yellow, 12 green, and 18 red. What is the probability
of selecting a green, a red, and a yellow or a red, yellow, and blue egg?
48.________
49. A die is rolled 3 times. What is the probability of getting two fours and a five?
49.________

ANSWERS
1a. 456,976,000
1b. 258,336,000
5. 420
9. 34,650
13. 27,885
17. 9
20. 64x 3 – 48x 2 + 12x – 1
22. 14909440x 12 y 3
13
26.
40
30. 17:3
34. 0.022
1
38.
6
2
42.
7
46. 0.00175
2a. 1,188,137,600
2b. 710,424,000
6. 17,297,280
10. 3,654
3. 120
11. 1001
7. 479,001,600
4. 30
8. 840
12. 65,780
14. 171,600 15. 103,776
18. 36 19. 5,527,200
21. 729x 6 -1458x 5 y +1215x 4 y 2 – 540x 3 y 3 + 135x 2 y 4 -18xy 5 + y 6
16. 20,358,520
23. 10500000x 3 24.
1
2
3
25.
8
1
27.
20
31. 13:7
35. 0.456
28. 1:19
32. 1:4
36. 0.087
29. 1:3
33. 3:1
37. 0.545
3
39.
52
13
43.
102
5
47.
13
40. 0.00075
44.
14
33
8
48. with replacement:
225
18
48. w/o replacement:
473
41. 0.031
1
45.
52
1
49.
216